A general model for the evolution of non-equilibrium systems

The paper addresses the problem of the evolution of systems that are initially in a state of non-equilibrium. The model we propose leads to an equation of motion that starts from a rephrasing of the classical non-equilibrium Ginzburg-Landau equation by reinterpreting in the sense of an exergy evolution paradigm. This paper may be considered as a logical corollary to -and at the same time as an e conceptual extension of-the solution to the problem of the existence and quantification of a non-equilibrium exergy presented in previous articles by the present Authors. In previous papers it was shown that, if both energy and exergy are considered a priori concepts, the evolution of the exergy of a solid body subject to a sufficiently smooth relaxation process can be calculated for arbitrary initial temperature or concentration distributions with an accuracy that depends only on the information about the initial distribution of the system properties at the initial time and on the availability of proper material relations. It was shown that the non-equilibrium exergy, i.e., the extra ideal work that can be extracted from the body, relaxes to zero as the system tends to its equilibrium state, so that the total exergy content (given by the sum of non-equilibrium and equilibrium exergy) attains the value given by its classical definition. The evolution history depends of course on the imposed b.c. and on the “gradient” that drives the relaxation. In this paper, we formalize the dependence of the non-equilibrium exergy on its possible drivers (pressure, temperature or concentration gradients) and derive a general “equation of motion” that links the former to the latter. The solution is analytical, and therefore there is no need to postulate local equilibrium, as long as we are dealing with a continuum (scales sufficiently removed from the atomic ones). A few applications to ideal and real processes are presented and discussed, while the application of the method to more complex and industrially relevant cases is left for later studies. The paradigm is theoretically simple and the resulting model of relatively easy implementation: we therefore hope that applications of the proposed framework may be systematically developed in the fields of engineering and natural science, to gain a better insight into real non-equilibrium processes.